Integrality of $v$-adic Multiple Zeta Values

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In this article, we prove the integrality of v -adic multiple zeta values (MZVs). For any index \mathfrak{s}\in\mathbb{N}^r and finite place v\in A := \mathbb{F}_q[\theta] , Chang and Mishiba introduced the notion of the v -adic MZVs \zeta_A(\mathfrak{s})_v , which is a function field analogue of Furusho's p -adic MZVs. By estimating the v -adic valuation of \zeta_A(\mathfrak{s})_v , we show that \zeta_A(\mathfrak{s})_v is a v -adic integer for almost all v . This result can be viewed as a function field analogue of the integrality of p -adic MZVs, which was proved by Akagi–Hirose–Yasuda and Chatzistamatiou.